Abstract
Quadratic functional equations, bilinear forms equivalent to the quadratic equation, and some generalizations are treated in this chapter. Among the normed linear spaces (n.l.s.), inner product spaces (i.p.s.) play an important role. The interesting question when an n.l.s. is an i.p.s. led to several characterizations of i.p.s. starting with Frechet [291], Jordan and von Neumann [398], etc. Functional equations are instrumental in many characterizations. One of the objectives of the next chapter is to bring out the involvement of functional equations in various characterizations of i.p.s.
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